摘要
考虑求解线性不适定问题的多尺度压缩投影算法,采用具有矩阵压缩策略的多尺度Galerkin方法,对Nesterov加速后的Landweber迭代正则化方程进行离散,给出近似解的先验误差估计,并提出后验参数选择策略,确保近似解的最优收敛率.数值实验表明将Nesterov加速方案应用到有限维空间求解线性不适定问题时,Landweber迭代速度明显加快.
We consider a multiscale compression projection algorithm for solving linear ill-posed integral equations.Using the multiscale Galerkin method with matrix compression strategy,the Landweber iterative regularization equation accelerated by Nesterov is discretized.A priori error estimate of the approximate solution is given,and the posterior parameter selection strategy is proposed to ensure that the optimal convergence rate of the approximate solution.Numerical experiments show that when Nesterov acceleration scheme is applied to solve linear ill-posed problems in finite dimensional space,Landweber iteration speed is obviously accelerated.
作者
江伟娟
罗兴钧
张荣
JIANG Weijuan;LUO Xingjun;ZHANG Rong(School of Mathematics and Computer Science,Gannan Normal University,Ganzhou 341000,China)
出处
《赣南师范大学学报》
2021年第6期12-18,共7页
Journal of Gannan Normal University
基金
国家自然科学基金(11761010)
赣南师范大学研究生创新专项项目(YCX19A026)。
